Type II blowup of solutions to a simplified Keller–Segel system in two dimensional domains Original Research Article

We consider a parabolic–elliptic system which is introduced as a simplified version of the so-called Keller–Segel system. In particular, we consider the system in a bounded domain of two dimensional Euclidean space. In that situation, we can find solutions to the system blowing up in finite time. Then, these solutions become the sum of an L1L1-function and delta functions at the blowup time. As regards the blowup speed, there exists a radial solution whose blowup speed is faster than that of backward self-similar solutions. We refer to that blowup as Type II blowup. In this paper, we investigate whether finite time blowup solutions to the system exhibit Type II blowup or not.